Solve the System of Linear Equations Using Substitution Method

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: Solve the following system of equations (y ≠ 0):

2x − 3/y = 9  …… (1)

3x + 7/y = 2  …… (2)

Step 1: Substitute 1/y = z

Let 1/y = z

Then equations (1) and (2) become:

2x − 3z = 9  …… (3)

3x + 7z = 2  …… (4)

Step 2: Express One Variable in Terms of the Other

From equation (3):

2x = 9 + 3z

⇒ x = ^{9 + 3z}/₂  …… (5)

Step 3: Substitute the Value of x in Equation (4)

Substitute x from equation (5) into equation (4):

3( ^{9 + 3z}/₂ ) + 7z = 2

Multiply the whole equation by 2:

27 + 9z + 14z = 4

27 + 23z = 4

23z = −23

⇒ z = −1

Step 4: Find the Value of y

Since z = 1/y,

1/y = −1

⇒ y = −1

Step 5: Find the Value of x

Substitute z = −1 in equation (5):

x = ^{9 + 3(−1)}/₂

x = ⁶/₂

x = 3

Final Answer

∴ The solution of the given system of equations is:

x = 3 and y = −1

Conclusion

Thus, by substituting 1/y = z and using the substitution method, we find that the solution of the given system of equations is (3, −1).